GATE (TF) Textile 2006 Question Paper Solution | GATE/2006/TF/31

Question 31 (Textile Engineering & Fibre Science)

The direct twist factor of a single 29.5 tex P/V yarn is 38.28 tpcm.tex^1/2. To keep twist per unit length same, the indirect cotton twist multiplier (tpi.Ne^-1/2) of 30 Ne cotton yarn will be approximately

(A)	2.95
(B)	3.27
(C)	2.27
(D)	3.83

[Show Answer]

Option B is correct.

Given in the question-

Direct twist factor(T.F) of P/V single yarn= $38.28 tpcm \times tex^\frac{1}{2}$

Count of P/V yarn(N1)=29.5 tex

Indirect cotton twist multiplier(TM)=?

Count of yarn(N2)=30s Ne

Now,

$TPCM=\frac{TF}{\sqrt count(N_1)}$

$TPCM=\frac{38.28}{\sqrt count(29.5)}$

$TPCM=\frac{38.28}{5.43}$

TPCM=7.049

TPI=7.049 x 2.54

TPI=17.90

To keep twist per unit length same-

$TPI=TM \times \sqrt Ne$

$17.90=TM \times \sqrt 30$

$17.90=TM \times 5.48$

$TM=\frac{17.90}{5.48}$

TM=3.27 (Ans)

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